This paper analyzes the robustness properties of 2D chaotic map image encryption schemes. We investigate the behavior of such block ciphers under different channel error types and find the transmission error robustness to be highly dependent on on the type of error occurring and to be very different as compared to the effects when using traditional block ciphers like AES. Additionally, chaotic-mixing-based encryption schemes are shown to be robust to lossy compression as long as the security requirements are not too high. This property facilitates the application of these ciphers in scenarios where lossy compression is applied to encrypted material, which is impossible in case traditional ciphers should be employed. If high security is required chaotic mixing loses its robustness to transmission errors and compression, still the lower computational demand may be an argument in favor of chaotic mixing as compared to traditional ciphers when visual data is to be encrypted.